This paper describes the admissible classes of parametric distribution functions of return portfolios and analyzes their consistency with the maximization of the expected utility. In particular, we present a general theory and a unifying framework with the following aims: (1) studying the implications of the classical market restrictions on the portfolio distributions; (2) establishing general rules of ordering, when the uncertain prospect depends by a finite number of parameters; (3) understanding how a dispersion measure has to be used, in order to obtain the investors' optimal portfolios.